Permanent magnet rotating electric machine and electric power steering device using the same

ABSTRACT

A permanent magnet rotating electric machine includes: a stator including: a stator core having teeth, and an armature winding wound around each of the teeth to configure the multiple phases; and a rotor including a rotor core, and permanent magnets provided in order around the rotor core. The rotor is arranged to be spaced apart from the stator with an air gap therebetween. Each of the permanent magnets has a curved surface opposed to the stator and is configured to satisfy the following relationship: 
     
       
         
           
             0.65 
             ≤ 
             
               
                 Rm 
                 × 
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
               
               
                 W 
                 ⁡ 
                 
                   ( 
                   
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     + 
                     g 
                   
                   ) 
                 
               
             
             ≤ 
             1.37 
           
         
       
         
         
           
             where Rm denotes a radius of curvature of the curved surface, h 1  denotes a thickness of a central portion of the permanent magnet in the peripheral direction, W denotes a width of the permanent magnet in the peripheral direction, and g denotes an air gap length of the air gap.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a permanent magnet rotating electricmachine, and more particularly to a motor for use in an electric powersteering device for automobile, for example.

2. Description of the Related Art

In the related-art permanent magnet rotating electric machine, a torquepulsation called a cogging torque occurs due to an interaction between astator core and a permanent magnet. Since the cogging torque causesvibration, it is strongly desired to decrease the cogging torque.Therefore, various techniques for decreasing the cogging torque havebeen proposed, and the configuration of permanent magnet to decrease thecogging torque has been examined. For example, as one example of a motorhaving twelve permanent magnets and nine magnetic poles, the curvedsurface of permanent magnet opposed to a stator is like a circular arc,the value of the radius of a rotor divided by the curvature of thesurface of permanent magnet opposed to the stator is set to the valuefor decreasing the cogging torque (e.g., refer to JP-A-2005-341688, page3-4, FIGS. 3 and 4). Also, a permanent magnet motor in which the numberof poles is 6 and the number of teeth is 18 has the center of outerdiameter eccentric so that the outer diameter of permanent magnetpassing the outside contour may be smaller than the outer diameter ofadjacent permanent magnet passing the vertex of contour, and the surfaceshape of the rotor is like a petal (e.g., refer to JP-A-2000-350393,page 3, FIG. 1).

In the related-art permanent magnet rotating electric machine, thoughthe cogging torque can be decreased by making the curved surface ofpermanent magnet opposed to the stator like a circular arc, there is aproblem that the height of the end portion of permanent magnet in theperipheral direction is smaller, whereby the irreversibledemagnetization at the end portion of permanent magnet in the peripheraldirection is likely to occur. When the permanent magnet rotatingelectric machine operates at the high temperature, there is anotherproblem that the irreversible demagnetization is more likely to occurbecause the coercive force of permanent magnet is decreased. If theirreversible demagnetization occurs, the torque is decreased, and thecogging torque and the torque ripple are increased because the magneticflux produced by the permanent magnet is different from at the time ofdesign, causing the vibration or noise. Therefore, if it is used for theelectric power steering device for automobile, the good steering feelingcan not be obtained.

SUMMARY OF THE INVENTION

This invention has been made to solve the above-mentioned problems, andit is an aspect of the present invention to provide a permanent magnetrotating electric machine in which the cogging torque is decreased andalso the irreversible demagnetization is decreased.

An embodiment of the present invention provides a permanent magnetrotating electric machine including: a stator including a stator corehaving a plurality of teeth, and an armature winding wound around eachof the plurality of teeth to configure the multiple phases; and a rotorincluding a rotor core, and a plurality of permanent magnets provided inorder in a peripheral direction around the rotor core. The rotor isarranged to be spaced apart from the stator with an air gaptherebetween. Each of the permanent magnets has a curved surface opposedto the stator and is configured to satisfy the following relationship:

$0.65 \leq \frac{{Rm} \times h\; 1}{W\left( {{h\; 1} + g} \right)} \leq 1.37$

where Rm denotes a radius of curvature of the curved surface, h1 denotesa thickness of a central portion of the permanent magnet in theperipheral direction, W denotes a width of the permanent magnet in theperipheral direction, and g denotes an air gap length of the air gap.

Another embodiment of the present invention provides a permanent magnetrotating electric machine including: a stator including a stator corehaving a plurality of teeth, and an armature winding wound around eachof the plurality of teeth to configure the multiple phases; and a rotorincluding: a rotor core, and a plurality of permanent magnets providedin order in a peripheral direction around the rotor core. The rotor isarranged to be spaced apart from the stator with an air gaptherebetween. Each of the permanent magnets has a curved surface opposedto the stator and is configured to satisfy the following relationship:

$0.40 \leq \frac{h\; 2}{h\; 1} \leq 0.73$

where h1 denotes a thickness of a central portion of the permanentmagnet in the peripheral direction, and h2 denotes a thickness of an endportion of the permanent magnet in the peripheral direction.

Since a permanent magnet rotating electric machine according to theinvention has a plurality of permanent magnets provided in order in theperipheral direction around the rotor core, with a curved surface of thepermanent magnet opposed to the stator having a radius of curvature Rm,and has the geometry satisfying the relationship 0.65≦Rm×h1/W(h1+g)≦1.37where the thickness of a central portion of the permanent magnet in theperipheral direction is h1, the width of the permanent magnet in theperipheral direction is W, and the air gap length between the stator andthe rotor is g, the cogging torque can be decreased and the irreversibledemagnetization can be decreased even by passing current through thearmature winding at the high temperature.

Also, since a permanent magnet rotating electric machine according tothe invention has a plurality of permanent magnets provided in order inthe peripheral direction around the rotor core, with a curved surface ofthe permanent magnet opposed to the stator, and has the geometrysatisfying the relationship 0.40≦h2/h1≦0.73 where the thickness of acentral portion of the permanent magnet in the peripheral direction ish1 and the thickness of an end portion of the permanent magnet in theperipheral direction is h2, the cogging torque can be decreased and theirreversible demagnetization can be decreased even by passing currentthrough the armature winding at the high temperature.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:

FIG. 1 is a constitutional view of a permanent magnet rotating electricmachine according to an embodiment 1 of the present invention;

FIG. 2 is a connection diagram of armature windings according to theembodiment 1 of the invention;

FIG. 3 is a partial enlarged view of the permanent magnet rotatingelectric machine according to the embodiment 1 of the invention;

FIG. 4 is a constitutional view of a rotor according to the embodiment 1of the present invention;

FIG. 5 is a view showing one example of the relationship between thewidth W of a permanent magnet and a demagnetizing factor;

FIG. 6 is a view showing one example of the relationship among ademagnetization evaluation parameter, the cogging torque and thedemagnetizing factor of permanent magnet according to the embodiment 1of the invention;

FIG. 7 is a view showing the waveform of cogging torque according to theembodiment 1 of the invention;

FIG. 8 is a view showing the relationship among the thickness ofpermanent magnet, the cogging torque and the demagnetizing factor ofpermanent magnet according to the embodiment 1 of the invention;

FIGS. 9A and 9B are partial enlarged views of a rotor according to anembodiment 2 of the invention;

FIG. 10 is a view showing the relationship between the ratio of theheight of a projection portion to the height of an end portion ofpermanent magnet in the peripheral direction and the demagnetizingfactor of permanent magnet according to the embodiment 2 of theinvention;

FIG. 11 is a constitutional view of a permanent magnet rotating electricmachine according to an embodiment 3 of the invention;

FIG. 12 is a constitutional view of another permanent magnet rotatingelectric machine according to the embodiment 3 of the invention;

FIG. 13 is a constitutional view of a permanent magnet rotating electricmachine according to an embodiment 4 of the invention;

FIG. 14 is a view showing the waveform of cogging torque according tothe embodiment 4 of the invention;

FIG. 15 is a constitutional view of a rotor according to an embodiment 5of the invention;

FIG. 16 is a constitutional view of another rotor according to theembodiment 5 of the invention;

FIG. 17 is a constitutional view of the conventional rotor; and

FIG. 18 is a concept view of an electric power steering device forvehicle using a permanent magnet rotating electric machine according toan embodiment 6 of the invention.

DETAILED DESCRIPTION OF THE INVENTION Embodiment 1

FIG. 1 is a constitutional view of a permanent magnet rotating electricmachine according to an embodiment 1 of the present invention, showingthe cross section of the permanent magnet rotating electric machine asseen from the axial direction. In FIG. 1, the permanent magnet rotatingelectric machine is shown in a simplified form by omitting the detailedparts of a frame or insulator, and a metallic tube for preventing thescattering of magnet. A stator core 1 has teeth 2 projecting inward. Theteeth 2 are arranged in the peripheral direction. The permanent magnetrotating electric machine is composed of a stator and a rotor, in whichthe rotor is arranged to be spaced apart from the stator with an gap ofan air gap length g therebetween. The gap length g is defined as thedistance between the stator opposed surface of a permanent magnet 4 andthe top end of the teeth 2, as shown in FIG. 1. The stator comprises astator core 1, the teeth 2, and an armature winding 3. The armaturewinding 3 is wound around each of the plurality of teeth 2 to configuremultiple phases. In FIG. 1, twelve teeth 2 are arranged, and thearmature winding 3 is wound in concentrated winding around each of theteeth 2.

On the other hand, the rotor comprises the permanent magnet 4, a rotorcore 5 and a shaft 6. In FIG. 1, ten permanent magnets 4 are arranged inthe peripheral direction around the rotor core 5. In the permanentmagnet rotating electric machine of this embodiment, the number of polesis 10 and the number of teeth is 12. Herein, the number of poles is thenumber of magnetic poles formed by the plurality of permanent magnets 4.Also, the shaft 6 is inserted into a central portion of the rotor core5. The stator core 1 and the rotor core 5 are made of magnetic material,and produced by laminating the electromagnetic steel plates, forexample. The rotor core 5 may be produced by cutting a solid core.

There are twelve armature windings 3, which are arranged in the order ofU+, U−, V−, V+, W+, W−, U−, U+, V+, V−, W− and W+. Herein, + and −indicate that the winding direction is reverse. With this arrangement,the armature windings 3 are configured in a total of three phases,including the U phase, the V phase and the W phase. In the connection ofthe armature winding 3, two armature windings connected in series arefurther connected in parallel to make the connection in each phase, inwhich the connection in each phase is delta connected, as shown in FIG.2. The delta connection may be substituted with the star connection, orthe armature windings in the connection in each phase may be connectednot in parallel but in series. In the case where the permanent magnetrotating electric machine is applied to the electric power steering forautomobile, it is mostly driven at a battery voltage of 12 V, and thedelta connection has more number of windings by about √3 times than thestart connection, so that the line diameter of the armature winding 3can be thinner accordingly, improving the winding workability. However,when the rotating electric machine is driven at a higher voltage thanthe battery voltage, the star connection may be used.

In the permanent magnet rotating electric machine with such aconfiguration, there is a method for making a curved surface of thepermanent magnet opposed to the stator like a circular arc to decreasethe cogging torque occurring due to an interaction between the permanentmagnet and the stator core as described in reference documents 1 and 2.However, in the permanent magnet rotating electric machine in which thecurved surface of the permanent magnet opposed to the stator is like acircular arc, the height of an end portion of the permanent magnet inthe peripheral direction is smaller, so that the irreversibledemagnetization is likely to occur at the end portion of the permanentmagnet in the peripheral direction. Also, when the permanent magnetrotating electric machine is operated at the high temperature, thecoercive force of the permanent magnet is decreased, whereby theirreversible demagnetization is more likely to occur.

Herein, the relationship between the demagnetization of the permanentmagnet and the arrangement of armature windings will be considered.First of all, an inverse magnetic field due to an armature current inwhich the armature windings in different phases are adjacent will beexplained. For example, in the case of the permanent magnet rotatingelectric machine in which the number of poles is 8 and the number ofteeth is 12, the arrangement of the armature windings is in the order ofU, V, W, U, V, W, U, V, W, U, V and W. Also, in the case of thepermanent magnet rotating electric machine in which the number of polesis 12 and the number of teeth is 9, the arrangement of the armaturewindings is in the order of U, W, V, U, W, V, U, W and V. In this way,when the different phases are adjacent, even if the maximum currentflows through the U phase, the current flowing through adjacent V phaseand W phase has as small as half the amplitude of the current flowingthrough the U phase. Also, the current having the same amplitude flowsthrough the adjacent armature windings, when the current in any phasebecomes zero. Considering that three phases are displaced from eachother by 120 degrees, the current having the same amplitude has theamplitude of Cos 30° times or √3/2 times the maximum current.

On the other hand, in the case of the permanent magnet rotating electricmachine in which the number of poles is 10 and the number of teeth is 12as in this embodiment, the armature windings 3 wound in the same phaseand in reverse direction around the adjacent teeth 2 are arranged, asshown in FIG. 1. For example, U+ and U− are adjacent. With such anarrangement, when the maximum current flows in any phase, a largeinverse magnetic field is applied to the permanent magnet 4 near theteeth 2 around which the armature winding 3 is wound in that phase. Interms of the current condition, in the case where the number of poles is10 and the number of teeth is 12, there is the same effect that a largercurrent by 3/√2 times=about 1.15 times flows through the armaturewinding than the armature windings in different phases are adjacent inthe case where the number of poles is 8 and the number of teeth is 12.That is, the rotating electric machine in which the number of poles is10 and the number of teeth is 12, the irreversible demagnetization ismore likely to occur about 1.15 times in the current condition than therotating electric machine in which the number of poles is 8 and thenumber of teeth is 12. Since the irreversible demagnetization rapidlyincreases beyond the limit of coercive force, a difference of 1.15 timeshas an influence on the design.

Especially in the positional relationship where an end portion of thepermanent magnet in the peripheral direction is closer to a part onwhich this inverse magnetic field is applied, there is a problem thatthe irreversible demagnetization is likely to occur in the permanentmagnet. FIG. 3 is a partial enlarged view of the constitution of thepermanent magnet rotating electric machine, as seen from the axialdirection. The occurrence of irreversible demagnetization will bedescribed below, using FIG. 3. If the U phase current becomes themaximum, a magneto-motive force of a closed magnetic circuit 50 passingthrough the teeth of U+ and U− is greater. At this time, since a largeinverse magnetic field is applied to an end portion (end portion to theleft in FIG. 3) of the permanent magnet 4 a in the peripheral direction,the irreversible demagnetization is likely to occur. In the arrangementof armature windings wound in same phase and in reverse direction aroundthe adjacent teeth, the irreversible demagnetization is more likely tooccur. Thus, in the invention, the irreversible demagnetization does notoccur even in a state where such inverse magnetic field is applied.

FIG. 4 is a constitutional view of the rotor in which the permanentmagnet is arranged according to this embodiment. The permanent magnet 4has the geometry in which the surface opposed to the stator is like acircular arc. The width of this permanent magnet 4 in the peripheraldirection is W, the height of the central portion in the peripheraldirection is h1, and the height of the end portion in the peripheraldirection is h2. Also, the radius of curvature of circular arc in thepermanent magnet 4 is Rm, and the radius (distance from the axial centerto the stator opposed surface of the permanent magnet) of the rotor isRr. In the permanent magnet 4, if the radius of curvature Rm is larger,the height h2 of the end portion in the peripheral direction is larger,whereby the permanent magnet is closer to a plate. This means that ifthe radius of curvature Rm is larger, the amount of demagnetization atthe end portion of the permanent magnet 4 in the peripheral direction issmaller.

FIG. 5 shows one example of the relationship between the width W of thepermanent magnet and a demagnetizing factor. The demagnetizing factorrepresents the amount of demagnetization in the permanent magnet, or thepercentage of irreversible demagnetization to the magnetic flux densityB inside the permanent magnet. In FIG. 5, the width W of permanentmagnet is normalized by the radius Rr of the rotor. From FIG. 5, it canbe found that as the width of permanent magnet is larger, thedemagnetizing factor of permanent magnet is larger. Further, inconsideration of an air gap length g between the rotor and the stator,assuming that the residual magnetic flux density of permanent magnet isBr and the magnetic flux density inside the permanent magnet is B, thereis the relationship as represented by the expression (1).

$\begin{matrix}\left\lbrack {{Numerical}\mspace{14mu}{expression}\mspace{14mu} 1} \right\rbrack & \; \\{B = {\frac{h\;{1/\mu_{r}}}{{h\;{1/\mu_{r}}} + g}B_{r}}} & (1)\end{matrix}$

Herein, μ_(r) denotes the recoil relative magnetic permeability. μ_(r)is a value of about 1.05 for sintered magnet of neodymium rare earth.The expression (1) can be approximated by the expression (2).

$\begin{matrix}\left\lbrack {{Numerical}\mspace{14mu}{expression}\mspace{14mu} 2} \right\rbrack & \; \\{B = {\frac{h\; 1}{{h\; 1} + g}B_{r}}} & (2)\end{matrix}$

From the expression (2), as h1/(h1+g) is larger, the magnetic fluxdensity B inside the permanent magnet is larger, whereby it can be foundthat the irreversible demagnetization of the permanent magnet is lesslikely to occur. From these, in the invention, the optimal geometry ofthe permanent magnet is designed, using a demagnetization evaluationparameter as shown in the expression (3) as the parameter for evaluatingthe irreversible demagnetization of the permanent magnet.

$\begin{matrix}\left\lbrack {{Numerical}\mspace{14mu}{expression}\mspace{14mu} 3} \right\rbrack & \; \\\frac{{Rmh}\; 1}{W\left( {{h\; 1} + g} \right)} & (3)\end{matrix}$

This demagnetization evaluation parameter is configured by directlymultiplying the terms that increase in the amount of demagnetization atthe larger value or reciprocally multiplying the terms that decrease inthe amount of demagnetization at the larger value. FIG. 6 is a viewshowing the relationship of the cogging torque and the demagnetizingfactor designating the amount of demagnetization of permanent magnetwith the demagnetization evaluation parameter. In FIG. 6, the horizontalaxis shows the demagnetization evaluation parameter and the verticalaxis shows the cogging torque and the demagnetizing factor of permanentmagnet. The demagnetization was measured at a magnet temperature of 140°C. and the current was greater than the rated current of the rotatingelectric machine.

In the case where the permanent magnet rotating electric machine isbuilt into the electric power steering device for automobile, from theviewpoint of steering feeling of the steering wheel, the cogging torqueis 0.01 Nm or less, preferably 0.005 Nm or less. On the other hand, fromthe viewpoint of decreasing the torque or reducing the vibration ornoise caused by the increased cogging torque or torque ripple, it isdesirable that the demagnetizing factor is 1% or less. To satisfy bothconditions, it is required that the demagnetization evaluation parameterof the expression (3) falls within the range as indicated by theexpression (4), preferably within the range as indicated by theexpression (5), as seen from FIG. 6.

$\begin{matrix}\left\lbrack {{Numerical}\mspace{14mu}{expression}\mspace{14mu} 4} \right\rbrack & \; \\{0.65 \leq \frac{R_{m}h_{1}}{W\left( {h_{1} + g} \right)} \leq 1.37} & (4) \\\left\lbrack {{Numerical}\mspace{14mu}{expression}\mspace{14mu} 5} \right\rbrack & \; \\{0.65 \leq \frac{R_{m}h_{1}}{W\left( {h_{1} + g} \right)} \leq 1.12} & (5)\end{matrix}$

FIG. 7 shows an example of the waveform of cogging torque. In FIG. 7,the horizontal axis shows the rotation angle (electrical angle) of therotor and the vertical axis shows the cogging torque. The comparison ismade between the values of demagnetization evaluation parameter of 0.80and 1.80. At 0.80 within the range as indicated by the expression (4),the cogging torque can be decreased more greatly than at 1.80 outsidethe range.

Next, the relationship between the geometry of permanent magnet and theirreversible demagnetization of permanent magnet from another viewpointwill be described below. FIG. 8 shows the relationship among thethickness of permanent magnet, the cogging torque and the demagnetizingfactor of permanent magnet. In FIG. 8, the horizontal axis shows theratio h2/h1 of the thickness h1 of the central portion of permanentmagnet and the thickness h2 of the end portion in the peripheraldirection and the vertical axis shows the cogging torque and thedemagnetizing factor indicating the amount of demagnetization ofpermanent magnet. The cogging torque is 0.01 Nm or less, preferably0.005 Nm or less, as described above. On the other hand, it is desirablethat the demagnetizing factor is 1% or less. To satisfy both conditions,it is required that the thickness ratio h2/h1 falls within the range asindicated by the expression (6), preferably within the range asindicated by the expression (7), as seen from FIG. 8.

$\begin{matrix}\left\lbrack {{Numerical}\mspace{14mu}{expression}\mspace{14mu} 6} \right\rbrack & \; \\{0.40 \leq \frac{h\; 2}{h\; 1} \leq 0.73} & (6) \\\left\lbrack {{Numerical}\mspace{14mu}{expression}\mspace{14mu} 7} \right\rbrack & \; \\{0.40 \leq \frac{h\; 2}{h\; 1} \leq 0.65} & (7)\end{matrix}$

With the above constitution, the cogging torque can be decreased ascompared with the conventional example. Further, the irreversibledemagnetization of permanent magnet can be suppressed. In particular, inthe permanent magnet rotating electric machine in which the armaturewindings are wound in same phase and in reverse direction around theadjacent teeth, the cogging torque can be decreased by applying thisinvention, though the irreversible demagnetization tended to be largerthan adjacent teeth in different phases. Further, the irreversibledemagnetization can be decreased by passing current through the armaturewinding at the high temperature, whereby the torque ripple can bedecreased.

In the permanent magnet rotating electric machine in concentratedwinding in which the number of poles is 10 and the number of teeth is 12with the constitution of the embodiment, the winding factor is 0.933. Onthe contrary, in the permanent magnet rotating electric machine in whichthe number of poles is 8 and the number of teeth is 12 as conventionallywidely used, the winding factor is 0.866. Comparing both, the windingfactor is higher with the constitution of this embodiment. Also, theleast common multiple of the number of poles and the number of teeth is60 in the constitution of this embodiment, whereas it is 24 in the casewhere the number of poles is 8 and the number of teeth is 12 asconventionally widely used, whereby the least common multiple is largerin the constitution of this embodiment. The least common multiple of thenumber of poles and the number of teeth is the number of ripples in thecogging torque, when the rotor of the rotating electric machine isrevolved once. There is a tendency that as the least common multiple islarger, the cogging torque is smaller. Hence, the permanent magnetrotating electric machine with the constitution of this embodiment isthe rotating electric machine having smaller cogging torque.Accordingly, with the constitution of this embodiment, the coggingtorque can be decreased while the irreversible demagnetization can bedecreased as compared with the conventional example. Also, since thenumber of poles is 10 and the number of teeth is 12, the winding factorcan be increased, and the utilization efficiency of the magnetic fluxgenerated by the permanent magnet can be improved, whereby the permanentmagnet rotating electric machine with the reduced size and weight andhigher efficiency can be obtained.

Embodiment 2

FIGS. 9A and 9B are partially enlarged views of a rotor for a permanentmagnet rotating electric machine according to an embodiment 2 of theinvention, showing a part of the rotor in cross section as seen from theaxial direction. In the permanent magnet rotating electric machine ofthis embodiment, the shape of the projection portion provided betweenthe adjacent permanent magnets is set more minutely than in theembodiment 1. In FIGS. 9A and 9B, the same reference numerals designatethe same or like parts as in FIG. 1, which is common throughout theentire text of the specification. Also, the form of the componentrepresented throughout the entire text of the specification is onlyillustrative, but not limited to the description.

FIG. 9A shows a case for comparison where the projection portion is notprovided and FIG. 9B shows a case where the projection portion 7 isprovided between the adjacent permanent magnets 4. This projectionportion 7 is made of magnetic material, and projects from the rotor core5. For example, the projection portion 7 may be formed together inproducing the rotor core 5 by stamping an electromagnetic steel platewith mold, or the magnetic material may be added after producing therotor core 5.

Herein, assuming that the height of the projection portion 7 is h3 andthe height of the end portion of the permanent magnet 4 in theperipheral direction is h2, the relationship between the ratio h3/h2 andthe amount of demagnetization of the permanent magnet will be describedbelow. FIG. 10 shows the relationship between the height ratio h3/h2 andthe amount of demagnetization of the permanent magnet. In FIG. 10, thehorizontal axis shows the height ratio h3/h2, and the vertical axisshows a difference in the demagnetizing factor indicating the amount ofdemagnetization of the permanent magnet. The difference in thedemagnetizing factor is the difference in the amount of demagnetizationfor the magnetic flux B inside the permanent magnet. The difference inthe amount of demagnetization is a value of subtracting the amount ofdemagnetization in which the projection portion 7 is not provided fromthe amount of demagnetization in which the projection portion 7 isprovided. If the difference in the amount of demagnetization is thenegative value, it is indicated that the irreversible demagnetizationcan be relieved owing to the effect of the projection portion 7. As seenfrom FIG. 10, if the height ratio h3/h2 is within the range as indicatedby the expression (8), there is no influence of the irreversibledemagnetization. To prevent collision with the stator, it is requiredthat the height h3 of the projection portion 7 is set to less than theheight h1 of the central portion of the permanent magnet 4 in theperipheral direction.

$\begin{matrix}\left\lbrack {{Numerical}\mspace{14mu}{expression}\mspace{14mu} 8} \right\rbrack & \; \\{\frac{h\; 3}{h\; 2} \geq 0.38} & (8)\end{matrix}$

Since a part of the magnetic flux passing from the stator to the endportion of the permanent magnet 4 in the peripheral direction isdiverted around the projection portion 7 by providing the projectionportion 7 made of magnetic material, the magnetic flux passing the endportion of the permanent magnet 4 in the peripheral direction isdecreased. Therefore, the irreversible demagnetization is relieved. Withthe above constitution, the inverse magnetic field at the end portion ofthe permanent magnet 4 in the peripheral direction can be relaxed, sothat the amount of demagnetization can be decreased. Also, since theprojection portion 7 is provided between the adjacent permanent magnets4, the permanent magnet 4 can be easily positioned.

Embodiment 3

FIGS. 11 and 12 are the constitutional views of a permanent magnetrotating electric machine according to an embodiment 3 of the invention,showing the cross section of the permanent magnet rotating electricmachine as seen from the axial direction. The permanent magnet rotatingelectric machine of this embodiment is different in the number of polesand the number of teeth from the embodiment 1. Though the permanentmagnet rotating electric machine in which the number of poles is 10 andthe number of teeth is 12 has been described in the embodiment 1, theinvention is also applicable to other combinations of the number ofpoles and the number of teeth.

FIG. 11 shows the permanent magnet rotating electric machine in whichthe number of poles is 14 and the number of teeth is 12. There aretwelve armature windings 3, which are arranged in the order of U+, U−,W−, W+, V+, V−, U−, U+, W+, W−, V− and V+. Herein, + and − indicate thatthe winding direction is reverse. With this arrangement, the armaturewindings 3 are configured in a total of three phases, including the Uphase, the V phase and the W phase. In the connection of the armaturewinding 3, two armature windings connected in series are furtherconnected in parallel to make the connection in each phase, in which theconnection in each phase is delta connected. The delta connection may besubstituted with the star connection, or the armature windings in theconnection in each phase may be connected not in parallel but in series.

In this case, since the armature windings 3 are wound in same phase andin reverse direction around the adjacent teeth 2, when the maximumcurrent flows in any phase, a large inverse magnetic field is applied tothe permanent magnet 4 to generate the irreversible demagnetization atthe end portion of the permanent magnet in the peripheral direction, asdescribed in the embodiment 1. However, in this embodiment, thedemagnetization evaluation parameter is set to satisfy the expressions(4) and (5), or the thickness ratio h2/h1 of the permanent magnet is setto satisfy the expressions (6) and (7), as described in the embodiment1, or the height ratio h3/h2 of the projection portion to the height ofthe end portion of the permanent magnet in the peripheral direction isset to satisfy the expression (8) as described in the embodiment 2.Thereby, the cogging torque can be decreased as compared with theconventional permanent magnet rotating electric machine. Further, theirreversible demagnetization can be decreased by passing current throughthe armature winding 3 at the high temperature, whereby the torqueripple can be decreased.

Also, the invention can be applied to other combinations of the numberof poles and the number of teeth. FIG. 12 shows the permanent magnetrotating electric machine in which the number of poles is 8 and thenumber of teeth is 9. In this case, there are nine armature windings 3,which are arranged in the order of U+, U−, U+, V+, V−, V+, W+, W− andW+. Herein, + and − indicate that the winding direction is reverse. U+,U− and U+ are connected in series to configure the U phase. Similarly,three windings are connected in series to configure the V phase and theW phase. And the three phases are delta connected or star connected.Even in this permanent magnet rotating electric machine, since thearmature windings 3 wound in same phase and in reverse direction arearranged around the adjacent teeth 2, when the current in any phasebecomes maximum, a large inverse magnetic field is applied to thepermanent magnet 4. Therefore, with the permanent magnet 4 having thegeometry satisfying the expressions (4) to (8), the cogging torque canbe decreased as compared with the conventional permanent magnet rotatingelectric machine. Further, the irreversible demagnetization can bedecreased by passing current through the armature winding 3 at the hightemperature, whereby the torque ripple can be decreased.

In addition, another permanent magnet rotating electric machine in whichthe number of poles is 10 and the number of teeth is 9, not shown, canachieve the same effect. Generally, in the permanent magnet rotatingelectric machine with the number of poles and the number of teeth suchthatNumber of poles:number of teeth=12n±2n:12nNumber of poles:number of teeth=9n±n:9n

(n: integer of 1 or greater)

the armature windings 3 wound in same phase and in reverse direction arearranged around the adjacent teeth, and with the permanent magnet havingthe geometry satisfying the expressions (4) to (8), the cogging torquecan be decreased. Further, the irreversible demagnetization can bedecreased by passing current through the armature winding 3 at the hightemperature, whereby the torque ripple can be decreased.

And in the permanent magnet rotating electric machine in concentratedwinding in which the number of poles is 14 and the number of teeth is12, the winding factor is 0.933 and the least common multiple of thenumber of poles and the number of teeth is 84. Since this value islarger than the permanent magnet rotating electric machine in which thenumber of poles is 8 and the number of teeth is 12 as conventionallywidely used, the constitution of this embodiment has the smaller coggingtorque and the larger winding factor than the conventional example,whereby the more efficient permanent magnet rotating electric machinewith the reduced size and weight can be produced. Also, in the permanentmagnet rotating electric machine in concentrated winding in which thenumber of poles is 8 and the number of teeth is 9, the winding factor is0.946 and the least common multiple of the number of poles and thenumber of teeth is 72. Moreover, in the permanent magnet rotatingelectric machine in concentrated winding in which the number of poles is10 and the number of teeth is 9, the winding factor is 0.946 and theleast common multiple of the number of poles and the number of teeth is90. Since these values are larger than the winding factor 0.866 and theleast common multiple 36 of the number of poles and the number of teethin the permanent magnet rotating electric machine in which the number ofpoles is 12 and the number of teeth is 9 as conventionally widely used,the constitution of this embodiment has the smaller cogging torque andthe larger winding factor, whereby the more efficient permanent magnetrotating electric machine with the reduced size and weight can beproduced.

From the above, in the permanent magnet rotating electric machine inwhich the number of poles is 10 and the number of teeth is 12, thepermanent magnet rotating electric machine in which the number of polesis 14 and the number of teeth is 12, and the permanent magnet rotatingelectric machine in which the number of poles is 8 and the number ofteeth is 9, the windings wound in same phase and in reverse directionare arranged around the adjacent teeth, and the permanent magnet has thegeometry satisfying the expressions (4) to (8), whereby the coggingtorque can be decreased. Further, the irreversible demagnetization canbe decreased by passing current through the armature winding 3 at thehigh temperature, whereby the torque ripple can be decreased. Therefore,the invention can be applied to the combinations of the number N ofpoles and the number M of teeth as represented by the followingexpression (9), in which the armature windings are wound in same phaseand in reverse direction.[Numerical expression 9]6/7≦M/N≦6/5  (9)where N and M are different integers. Also, in the conventionalpermanent magnet rotating electric machine with the combination of thenumber N of poles and the number M of teeth which does not require thatthe armature windings are wound in same phase and in reverse direction,the invention has low effect of application. Therefore, the number N ofpoles and the number M of teeth may be combined within the range asrepresented by the following expression (10), except for thecombinations of the number N of poles and the number M of teeth in theconventional permanent magnet rotating electric machine.[Numerical expression 10]3/4<M/N<3/2  (10)

Embodiment 4

FIG. 13 is a constitutional view of a permanent magnet rotating electricmachine according to an embodiment 4 of the invention, showing the crosssection of the permanent magnet rotating electric machine as seen fromthe axial direction. The permanent magnet rotating electric machine ofthis embodiment is different from the embodiment 1 in that the statorcore is constituted by connecting the split iron cores.

The stator core 11 is produced by concatenating the split iron cores inthe peripheral direction, not by stamping out a piece with mold. Variousproduction methods are conceived such as splitting the iron core intoeach tooth 12, as shown in FIG. 13, or stamping out a core back in theshape of a circle and fitting the teeth. In this way, in the case wherethe stator core 11 is composed of the split iron cores, there ispossibility that the precision or roundness of inner peripheral shape ofthe stator core 11 is worse than stamping out a piece with mold. If theshape precision of the stator core 11 is worse, the cogging torquecomponent with the same number of pulsations as the number of polesoccurs every time the rotor is rotated. Accordingly, when used for theelectric power steering device requiring the low cogging torque, it isnecessary to consider not only the cogging torque of the componentoccurring at the number of pulsations equivalent to the least commonmultiple of the number of poles and the number of teeth, but also thecogging torque of the component occurring at the same number ofpulsations as the number of poles every rotation.

However, if the permanent magnet 4 has the geometry satisfying theexpressions (4) to (8) as described in the embodiment 1, the coggingtorque component occurring at the number of pulsations equivalent to theleast common multiple of the number of poles and the number of teeth canbe sufficiently decreased. Therefore, even if there is the coggingtorque component at the same number of pulsations as the number of polesevery rotation, the permanent magnet rotating electric machine with lowcogging torque can be obtained.

FIG. 14 is a view showing a specific example of the waveform of coggingtorque for the permanent magnet rotating electric machine in which thenumber of poles is 10 and the number of teeth is 12, in which the statorcore is split. In the conventional permanent magnet rotating electricmachine, the cogging torque component having the number of pulsationsmatched with the least common multiple 60 of the number of poles and thenumber of teeth and the component pulsating ten times equal to thenumber of poles every rotation are large, and the amplitude of coggingtorque is large. However, in the permanent magnet rotating electricmachine of the invention, since the cogging torque component having thenumber of pulsations matched with the least common multiple 60 can besufficiently decreased, there is only the component pulsating 10 timesalmost equal to the number of poles. This indicates that the coggingtorque can be suppressed to be sufficiently small, even if the geometryprecision of the stator core 11 is bad.

Further, especially if the opening width of slot formed between theplurality of teeth is small by stamping out a piece with mold, it isdifficult to put the nozzle of a winding machine for winding thearmature winding into the slot, whereby it was difficult to improve thespace factor of the armature winding. However, when the stator core 11is constituted by the split stator core, the space factor of thearmature winding 3 can be improved even if the opening width of slot isso small that the copper loss and the coil end are reduced, whereby therotating electric machine has the reduced size and weight and is moreefficient.

Embodiment 5

FIGS. 15 and 16 are constitutional views of a rotor of a permanentmagnet rotating electric machine according to an embodiment 5 of theinvention, showing the cross section of the permanent magnet rotatingelectric machine as seen from the axial direction. The permanent magnetrotating electric machine of this embodiment is different from theembodiment 1 in that a metallic tube for preventing the scattering ofpermanent magnet is provided around the permanent magnet for the rotor.In FIGS. 15 and 16, the metallic tubes 8 and 9 for preventing thescattering of the permanent magnet 4 are provided to surround the rotorcore 5 and the plurality of permanent magnets 4. The metallic tube has arole of preventing the scattering of the permanent magnet 4 due to acentrifugal force when the rotor is rotated at high speed.

FIG. 17 is a constitutional view of the conventional permanent magnetrotating electric machine in which a metallic tube 28 is provided aroundthe periphery of a permanent magnet 24 for the rotor. Thecross-sectional shape of the permanent magnet 24 as seen from the axialdirection is rectangular, in which the permanent magnet 24 is protectedby the metallic tube 28 in contact with a part of the corner of thepermanent magnet 24. If a centrifugal force is applied, a strong stressis concentrated on the part in contact with the corner of the permanentmagnet 24, causing a problem that the metallic tube 28 is easy to break.Since the corner of the permanent magnet 24 is acute, the metallic tube28 is easily bruised in the manufacturing process, resulting in aproblem that the tube is easy to break due to this bruise. Inparticular, when the cross-sectional shape of the permanent magnet 24 isrectangular, the maximum outer diameter of the rotor including thepermanent magnet 24 becomes the part of the corner of the permanentmagnet 24, so that the metallic tube 28 is easy to contact this corner.

However, the curved surface of the permanent magnet 4 opposed to thestator is like a circular arc, and the permanent magnet 4 has thegeometry satisfying the expressions (4) to (8), as described in theembodiment 1, whereby the contact area between the permanent magnet 4and the metallic tube 8 can be increased, relaxing the stress, as shownin FIG. 15. Therefore, the metallic tube 8 is not easily bruised due toa centrifugal force. Also, the metallic tube 8 is not easily bruised inthe manufacturing process. For these reasons, the metallic tube 8 has astructure that can withstand the centrifugal force even if it is madethin. For example, the metallic tube 8 can be formed of the stainlesstube of 0.2 mm or less, or further 0.1 mm or less. By making themetallic tube 8 thinner, the air gap length between the rotor and thestator of the permanent magnet rotating electric machine can be reduced,so that the sufficient magnetic flux can be generated with the smallpermanent magnet 4, whereby the amount of using the material for thepermanent magnet 4 can be reduced. As a result, the permanent magnetrotating electric machine can be reduced in size and weight and be moreefficient. Even if the metallic tube 8 is provided, the air gap length gis defined as the distance between the stator opposed surface of thepermanent magnet 4 and the top end of the teeth 2.

Also, FIG. 16 is a constitutional view of a rotor of the permanentmagnet rotating electric machine in which the metallic tube is notcylindrical but roughly polygonal in cross section. The metallic tube 9,which is roughly polygonal in cross section, has the geometry conformingto the geometry of the permanent magnet 4 in a part corresponding to thecircular arc part of the permanent magnet 4 and almost straight betweenthe adjacent permanent magnets. With such geometry, the permanentmagnets 4 are contacted and connected by the metallic tube 9, increasingthe contact area between the metallic tube 9 and the permanent magnet 4,whereby even if the metallic tube 9 and the permanent magnet 4 generateheat due to eddy currents, the local temperature rise of the permanentmagnet 4 is alleviated to improve the demagnetization resistance of thepermanent magnet 4. Further, since the contact area between the metallictube 9 and the permanent magnet 4 is increased, the stress is relaxed,so that the metallic tube is stronger to the centrifugal force at highspeed rotation.

In FIG. 16, the metallic tube 9 is in contact with most of the circulararc part of the permanent magnet 4 conforming to the geometry of thepermanent magnet 4, but the geometry of the metallic tube is not limitedto this. For example, it may be in contact with some of the circular arcpart of the permanent magnet 4. If the contact area with the permanentmagnet 4 is larger than the metallic tube 8 as shown in FIG. 15, it isneedless to say that the local temperature rise is alleviated eventhough there is heat generation due to eddy currents.

Further, if the metallic tube is stainless, there is no influence on themagnetic circuit even with the polygonal shape in cross section, notcausing the generation of cogging torque, whereby the permanent magnetrotating electric machine with low cogging torque can be produced.

Embodiment 6

FIG. 18 is a concept view of an electric power steering device forvehicle using a permanent magnet rotating electric machine according toan embodiment 6 of the invention. In FIG. 18, the electric powersteering device is provided with a column shaft 31 for transmitting asteering effort from a steering wheel 30. The column shaft 31 isconnected to a worm gear 32 (the details are omitted but a gear box onlyis shown in FIG. 18) that transmits the output (torque, rpm) of a motor34 driven under a controller 33 by changing the rotational directionorthogonally, and at the same time slows down to increase an assisttorque. Reference numeral 35 denotes a handle joint for transmitting asteering effort and changing the rotational direction. Reference numeral36 denotes a steering gear (the details are omitted and the gear boxonly is shown in FIG. 18) that decelerates the rotation of the columnshaft 31 and at the same time converts it to the linear motion of a rack37 to obtain a desired displacement. With the linear motion of this rack37, the wheel can be moved to change the direction of the vehicle.

In such electric power steering device, a pulsation of torque generatedby the motor 34 is transmitted via the worm gear 32 and the column shaft31 to the steering wheel 30. Accordingly, when the motor 34 generates alarge torque pulsation, a smooth steering feeling can not be obtained.Also, if the electric motor generates a large cogging torque even in astate where it does not generate the torque for assist, the smoothsteering feeling can not be obtained.

However, the cogging torque can be decreased by incorporating thepermanent magnet rotating electric machine according to the invention asthe motor 34 of the electric power steering device of this embodiment.Also, since the irreversible demagnetization hardly occurs even bypassing current through the armature winding of the motor 34 at the hightemperature, the torque ripple causing the vibration or noise is alsodecreased. Therefore, the steering feeling in the electric powersteering device can be improved.

Also, since it is required that the motor for the electric powersteering device has the smaller size and the decreased amount of usingthe permanent magnet, the magnetic air gap length between the rotor andthe stator is mostly designed to be 1 mm or less. With such small airgap length, if the geometry of the permanent magnet is not appropriate,the irreversible demagnetization may occur at the temperature as high as140° C., for example. In particular, in the permanent magnet rotatingelectric machine with the relationshipNumber of poles:number of teeth=12n±2n:12nNumber of poles:number of teeth=9n±n:9n

(n: integer of 1 or greater)

the windings wound in same phase and in reverse direction is arrangedaround the adjacent teeth, whereby the irreversible demagnetization is aproblem. However, if the permanent magnet rotating electric machine asdescribed in the embodiments 1 to 5 is employed for the electric powersteering device, the irreversible demagnetization hardly occurs in thepermanent magnet, and the cogging torque can be smaller, whereby thesteering feeling can be improved. Also, the minimum common multiple ofthe number of poles and the number of teeth is larger and the windingfactor is also larger than the conventional permanent magnet rotatingelectric machine, and the cogging torque can be decreased, whereby themore efficient permanent magnet rotating electric machine with thereduced size and weight can be produced.

What is claimed is:
 1. A permanent magnet rotating electric machinecomprising: a stator including: a stator core having a plurality ofteeth; and an armature winding wound around each of the plurality ofteeth to configure multiple phases, wherein the armature windings arewound in same phase and in reverse directions around adjacent teeth; arotor having a radius Rr and including: a rotor core; and a plurality ofpermanent magnets provided in order in a peripheral direction around therotor core; and a roughly polygonal metal tube surrounding the rotor,wherein the rotor is arranged to be spaced apart from the stator with anair gap therebetween, and wherein each of the permanent magnets has acurved surface opposed to the stator and is configured to satisfy thefollowing relationship:$0.65 \leq \frac{{Rm} \times h\; 1}{W\left( {{h\; 1} + g} \right)} \leq 1.37$where Rm denotes a radius of curvature of the curved surface, h1 denotesa thickness of a central portion of the permanent magnet in theperipheral direction, W denotes a width of the permanent magnet in theperipheral direction, and g denotes an air gap length of the air gap,wherein Rm<Rr, and wherein the roughly polygonal metal tube surroundingthe rotor engages the curved surfaces of the permanent magnets opposedto the stator over the majority of the circumferential length of each ofthe permanent magnets and does not follow a circular arc, centered onthe center of radius Rr, at the circumferential locations of thepermanent magnets over the majority of the circumferential length ofeach of the permanent magnets, such that the roughly polygonal metaltube surrounding the rotor follows a convex circular arc centered on thecenter of radius Rm inside the metal tube over the majority of thecircumferential length of each of the permanent magnets, wherein therotor core includes a projection portion, and wherein the roughlypolygonal metal tube does not engage with the projection portion of therotor core, wherein the rotor core is polygonal, each of said permanentmagnets being provided on one of the polygonal surfaces, wherein theprojection portion is provided between two adjacent permanent magnets,is made of magnetic substance and projects from the polygonal surfacesto which said two adjacent permanent magnets are provided, wherein theprojection portion and each of the permanent magnets are configured tosatisfy the following relationships,h3/h2≧0.38 and h1≧h3 where h1 is as previously denoted, h2 denotes athickness of an end portion of the curved surface of the permanentmagnet in the peripheral direction, and h3 denotes a height of theprojection portion relative to the polygonal surfaces to which said twoof the permanent magnets are provided.
 2. The permanent magnet rotatingelectric machine according to claim 1, wherein the followingrelationship is satisfied6/7≦M/N≦6/5 where N denotes a number of magnetic poles formed by theplurality of permanent magnets, and M denotes a number of the teeth. 3.The permanent magnet rotating electric machine according to claim 1,wherein the following relationship is satisfied3/4<M/N<3/2 where N denotes a number of magnetic poles formed by theplurality of permanent magnets, and M denotes a number of the teeth. 4.The permanent magnet rotating electric machine according to claim 1,wherein the following relationship is satisfiedN:M=12n±2n:12n (n is an integer of 1 or greater) where N denotes anumber of magnetic poles formed by the plurality of permanent magnets,and M denotes a number of the teeth.
 5. The permanent magnet rotatingelectric machine according to claim 1, wherein the followingrelationship is satisfiedN:M=9n±n:9n (n is an integer of 1 or greater) where N denotes a numberof magnetic poles formed by the plurality of permanent magnets, and Mdenotes a number of the teeth.
 6. The permanent magnet rotating electricmachine according to claim 1, wherein the stator core is configured by aplurality of split iron cores.
 7. A permanent magnet rotating electricmachine comprising: a stator including: a stator core having a pluralityof teeth; and an armature winding wound around each of the plurality ofteeth to configure multiple phases, wherein the armature windings arewound in same phase and in reverse directions around adjacent teeth; anda rotor having a radius Rr and including: a rotor core; a plurality ofpermanent magnets provided in order in a peripheral direction around therotor core; and a roughly polygonal metal tube surrounding the rotor,wherein the rotor is arranged to be spaced apart from the stator with anair gap therebetween, wherein each of the permanent magnets has a curvedsurface opposed to the stator and is configured to satisfy the followingrelationship: $0.40 \leq \frac{h\; 2}{h\; 1} \leq 0.73$ where h1 denotesa thickness of a central portion of the permanent magnet in theperipheral direction, and h2 denotes a thickness of an end portion ofthe curved surface of the permanent magnet in the peripheral direction,wherein Rm<Rr, where Rm denotes a radius of curvature of the curvedsurface, and wherein the roughly polygonal metal tube surrounding therotor engages the curved surfaces of the permanent magnets opposed tothe stator over the majority of the circumferential length of each ofthe permanent magnets and does not follow a circular arc, centered onthe center of radius Rr, at the circumferential locations of thepermanent magnets over the majority of the circumferential length ofeach of the permanent magnets, such that the roughly polygonal metaltube surrounding the rotor follows a convex circular arc centered on thecenter of radius Rm inside the metal tube over the majority of thecircumferential length of each of the permanent magnets, wherein therotor core includes a projection portion, and wherein the roughlypolygonal metal tube does not engage with the projection portion of therotor core, wherein the rotor core is polygonal, each of said permanentmagnets being provided on one of the polygonal surfaces, wherein theprojection portion is provided between two adjacent permanent magnets,is made of magnetic substance and projects from the polygonal surfacesto which said two adjacent permanent magnets are provided, wherein theprojection portion and each of the permanent magnets are configured tosatisfy the following relationships,h3/h2≧0.38 and h1≧h3 where h1 and h2 are as previously denoted, and h3denotes a height of the projection portion relative to the polygonalsurfaces to which said two of the permanent magnets are provided.
 8. Thepermanent magnet rotating electric machine according to claim 7, whereinthe following relationship is satisfied6/7≦M/N≦6/5 where N denotes a number of magnetic poles formed by theplurality of permanent magnets, and M denotes a number of the teeth. 9.The permanent magnet rotating electric machine according to claim 7,wherein the following relationship is satisfied3/4<M/N<3/2 where N denotes a number of magnetic poles formed by theplurality of permanent magnets, and M denotes a number of the teeth. 10.The permanent magnet rotating electric machine according to claim 7,wherein the following relationship is satisfiedN:M=12n±2n:12n (n is an integer of 1 or greater) where N denotes anumber of magnetic poles formed by the plurality of permanent magnets,and M denotes a number of the teeth.
 11. The permanent magnet rotatingelectric machine according to claim 7, wherein the followingrelationship is satisfiedN:M=9n±n:9n (n is an integer of 1 or greater) where N denotes a numberof magnetic poles formed by the plurality of permanent magnets, and Mdenotes a number of the teeth.
 12. The permanent magnet rotatingelectric machine according to claim 7, wherein the stator core isconfigured by a plurality of split iron cores.
 13. The permanent magnetrotating electric machine according to claim 1, wherein the upper limitof the demagnetization evaluation parameter (Rm·h1)/(W(h1+g)) is 1.12.14. The permanent magnet rotating electric machine according to claim 1,wherein the roughly polygonal metal tube is almost straight atcircumferential locations between the permanent magnets.
 15. Thepermanent magnet rotating electric machine according to claim 7, whereinthe roughly polygonal metal tube is almost straight at circumferentiallocations between the permanent magnets.